Understanding Ceria Nanoparticles from First-Principles Calculations

10142

2007, 111, 10142-10145 Published on Web 06/22/2007

Understanding Ceria Nanoparticles from First-Principles Calculations Christoph Loschen,§,† Stefan T. Bromley,§ Konstantin M. Neyman,§,‡,* and Francesc Illas§ Departament de Quı´mica Fı´sica & Centre especial de Recerca en Quı´mica Teo´ rica, UniVersitat de Barcelona & Parc Cientı´fic de Barcelona, 08028 Barcelona, Spain, and Institucio´ Catalana de Recerca i Estudis AVanc¸ ats (ICREA), 08010 Barcelona, Spain ReceiVed: April 10, 2007; In Final Form: May 30, 2007

Octahedral clusters (CeO2-x)n (n e 85) have been studied using a density functional method (DFT+U) adapted to model nanocrystalline ceria. The binding energies of the clusters Ce19O32, Ce44O80, and Ce85O160 are shown to converge to the bulk limit almost linearly with respect to the average coordination number of Ce. The experimentally detected anomalous lattice expansion for nanoscale (CeO2-x)n particles of decreasing size is explicitly assigned to the presence of oxygen vacancies. Partially reduced Ce3+ cations are found to occupy more open edge and corner sites of the nanoparticles, whereas most oxidized Ce4+ centers are located in highly coordinated positions. This finding is crucial for the understanding of ceria reactivity at the nanoscale.

Ceria (cerium oxide, CeO2), one of the most reactive rareearth metal oxide materials, has drawn dramatically increased attention due to its particularly high performance in a variety of applications such as catalysis and fuel cells.1-3 Although in catalysis ceria is ubiquitously used as a support for deposited active metals, in many reactions, ceria is not simply inert but directly affects the catalytic processes. The reactivity of ceria is connected to its chemical reducibility (i.e., the interplay between the oxidation states Ce4+/Ce3+), which results in its capability for storing oxygen under oxidizing conditions and releasing it under reducing conditions. The very rapidly growing interest in ceria-based materials and the lack of a full understanding of their workings at a fundamental level presents a demanding challenge to theory to uncover the detailed microscopic picture of their surface structure and reactivity. Although classical theoretical studies have reported atomistic structure and energetics,4-7 pertinent electronic structure calculations of ceria, in particular, with defects, performed at a sufficiently accurate level of theory are still rather limited. This latter deficiency is largely due to the well-known difficulty of contemporary methods based on density functional theory (DFT) to properly describe localization of the Ce 4f electron in the reduced Ce3+ ionic form. This problem hampers the application of DFT to the most active forms of ceria (CeO2-x), which feature oxygen vacancies. Fortunately, practical, so-called DFT+U schemes8 based on the idea of the Hubbard Hamiltonian and allowing for a proper localization of strongly correlated electrons have recently become available for large-scale calculations. In the present computational approach, the Hubbard parameter U, which reflects the strength of the on-site Coulomb interaction, and the * To whom correspondence should be addressed. E-mail: konstantin. [email protected]. Fax: +34 93 402 1231. § Universitat de Barcelona & Parc Cientı´fic de Barcelona. † Present address: Henkel KGaA, Scientific Computing, D-40589 Du¨sseldorf, Germany. ‡ ICREA.

10.1021/jp072787m CCC: $37.00

parameter J, which adjusts the strength of the exchange interaction, are combined into a single parameter Ueff ) U J,9 the optimal value of which depends on the system and property under consideration.10 DFT+U studies have been shown to provide a sufficiently accurate description of the range of materials, CeO2 to Ce2O3.10,11 Computationally more demanding DFT schemes, using hybrid exchange-correlation functionals, offer alternative solutions.12,13 Compared to the bulk, quite different properties are expected for nanoscale particles, primarily due to (quantum) size effects and exposed low-coordinated surface sites.14 Effects of the nanocrystallinity of CeO2-x supports on catalytic performance can be indeed drastic. For instance, by depositing Au on nanocrystalline CeO2-x particles of ∼4 nm diameter, an increase of 2 orders of magnitude in the CO oxidation activity has been achieved relative to bulk CeO2/Au catalysts.3 The chemical impact of ceria changes severely when its size is decreased to the nanometer dimension, whereupon it appears to act as a highly active component, improving the overall catalytic performance. This example implies the need for nanoparticle models of ceria (and other oxides) in theoretical catalysisrelevant studies, with respect to commonly used extended surface models. Although nanoparticle models have been developed15 and fruitfully applied for a DFT description of model metal catalysts,16-18 similar first-principles systematic studies of moderately large oxide particles of catalytic relevance are not yet available. The recent ability to precisely prepare small ceria nanoparticles and their assemblies with controlled tailormade morphologies using dedicated chemical approaches19-20 presents a unique opportunity for high-level calculations to provide microscopic insight into these well-defined systems. In this Letter, we design a series of nanoparticle models Ce19O32, Ce44O80, and Ce85O160 representing nanocrystalline ceria species of practical importance and explore their properties with the help of a state-of-the-art plane wave DFT+U method. This methodology allows us to follow the convergence of the cluster binding energies to the bulk limit and, further, to © 2007 American Chemical Society

Letters

Figure 1. Studied octahedral (CeO2-x)n nanoparticles of growing size, which are cut by (111) planes from the bulk CeO2; (a) Ce19O32 (x ) 0.32), (b) Ce44O80 (x ) 0.18), and (c) Ce85O160 (x ) 0.12).

explicitly assign the detected anomalous lattice expansion in nanoscale ceria particles of decreasing size21 to the presence of defects. Furthermore, partially reduced Ce cations (formal charge 3+) are demonstrated to occupy more open sites on the nanoparticles, whereas Ce4+ cations are located in highly coordinated positions. DFT+U calculations were performed using the program package VASP,22,23 with the following computational details established by us elsewhere:10 plane wave basis with a cutoff of 415 eV for the kinetic energy, projector-augmented wave account of core-valence electron interactions.24 The nanoparticles were separated by ∼1 nm from each other in periodic arrays to avoid interactions, and calculations were performed at the Γ-point. Exchange-correlation functionals of both LDA (VWN25) and GGA (PW9126) types were employed, with Ueff ) 5 and 3 eV, respectively.10 GGA interatomic distances in CeO2 and Ce2O3 were calculated to be notably overestimated.10 Thus, the computational procedure chosen in this work was to optimize structures with the LDA functional, for which the GGA energy was subsequently computed in a single-point fashion. The total energy tolerance used to define self-consistency of electron density was 10-4 eV. Structures were optimized until the total energy differences of subsequent relaxation steps became less than 10-3 eV. The design of representative structural models for ceria nanoparticles is delicate due to numerous possible atomic configurations. In line with experimental findings,19,20 dedicated models were chosen to feature atomic configurations of the CeO2 bulk, to expose most stable O-terminated {111} facets, and to be octahedral, although the main conclusions of this study are considered to be valid for cuboctahedral clusters also. These preconditions result in a series of well-defined nanoparticles (CeO2-x)n, x e 0.5, the smallest of which are studied here (Figure 1), Ce19O32, Ce44O80, and Ce85O160 reaching a diameter of ∼2 nm. The present choice of the particle shape is also justified via calculations using a well-tested set of empirical pair potentials that allow for the treatment of both stoichiometric and reduced ceria systems.4 These potentials have been employed for stoichiometric nanoclusters in other studies showing that the evolution to bulk-like ceria occurs relatively rapidly. For (CeO2)n clusters generated via simulated annealing calculations, indications of a bulk-like structure for clusters as small as n ) 10 can be discerned; the clusters gradually evolve to fully bulk-

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Figure 2. Dependence of experimental33 and calculated “lattice constant” a0 of ceria nanoparticles on the particle diameter D. For calculated particles, the lattice constant was derived from the average Ce-Ce distance, a0 ) x2 dCe-Ce. The inset shows the correlation of the binding energy Eb (eV) of the nanoparticles per Ce atom with the average coordination number of Ce atoms; Eb(LDA+U) ) -2.505-1.079 × , Eb(GGA+U) ) -3.367-0.905 × .

like ones for n ) 50, which already exhibit characteristic {111} facets.5 The relatively rapid transition to bulk-like structure is probably due to the pronounced ionic character of the interatomic interactions in ceria, at variance with more covalent oxides such as SiO2.27 For considerably larger ceria clusters containing thousands of atoms, amorphization-recrystallization simulations using the potentials have yielded {100}-truncated octahedral cluster morphologies28 in good agreement with experimental TEM images.20 Using the basin-hopping29 global optimization technique and the same potentials, we have also studied the low-energy isomer landscape of the nonstoichiometric Ce19O32 cluster. The lowest energy isomer we could find is precisely the octahedral cluster shown in Figure 1a, with the next two higher energy Ce19O32 clusters both also preserving bulk-like features. This prediction of energetic isomer ordering was confirmed by our DFT+U calculations, where the two higher energy Ce19O32 isomers were also found to be g2 eV above the octahedral ground-state structure. Thus, we are confident that essential properties of moderately large ceria nanoparticles can be adequately described using the bulk-derived octahedral models. Calculated (LDA+U) average interatomic distances reveal a monotonic elongation for larger clusters, Ce19O32 < Ce44O80 < Ce85O160, from 364 to 373 pm (Ce-Ce) and from 228 to 230 pm (Ce-O). This corresponds to a smooth convergence toward the bulk values of 382 and 234 pm, respectively. An analogous trend follows from the pair potential calculations of stoichiometric ceria particles.5 Such a lattice expansion with increasing size is also typical for metal nanoparticles.15 However, according to electron diffraction findings, the lattice constant of nanostructured ceria decreases toward the bulk value with increasing particle size.21 This so-called “lattice anomaly” has been confirmed by other methods.30-32 The size of this effect also depends on the synthesis procedure and on the shape of the particles.33 The discrepancy is illustrated in Figure 2, where the DFT+U and experimental lattice constants are plotted against the particle size. Although the synthesized and the calculated clusters are of somewhat different sizes, the clearly opposed trends are expected to hold for the whole range of the cluster sizes. The reason for the lattice expansion is suggested to be the increasing amount of Ce3+ at the surface of smaller clusters, thereby

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TABLE 1: Average LDA+U Ce-Ce Distancesa (dCe-Ce, pm) in Regular Nanoparticles Ce19O32 and Ce44O80 and their Derivatives with O Vacancies in the Outer (Xout) or Inner (Xin) Cluster Shells Ce19O32

Ce19O31Xin

Ce19O31Xout

Ce44O80

Ce44O79Xout

364

365 383

366 396

370

370 403

dCe-Ce dXCe-Ce

a The dXCe-Ce values are for Ce atoms surrounding the vacancy X; dCe-Ce ) 382 pm for bulk CeO2.

TABLE 2: Position of Ce Atom in the CeO2-x System, the Number of Atoms in this Position (#Ce), the Energies of the Ce 3d Core Levels (E3d), and the Magnetic Moment [µ(Ce)]; Values are Averaged over Symmetry-Equivalent Positions system CeO2 Ce2O3 Ce19O32 Ce44O80

Ce85O160

position bulk bulk corner edge inside corner edge facet inside corner edge facet inside

#Ce

3d/eV

µ(Ce)/µB

1 2 6 12 1 6 24 8 6 6 36 24 19

-867.0 -861.8 -863.6 -863.8 -868.0 -865.1 -864.6 -867.7 -867.8 -860.7 -863.2 -866.2 -866.3

0.00 0.96 0.69 0.68 0.01 0.47 0.56 0.02 0.03 0.70 0.41 0.03 0.04

reducing the Ce-O electrostatic attraction.21 Indeed, it was shown that the ratio Ce3+/Ce4+ is higher for smaller clusters.32,34 Since the particles studied in this work contain reduced surface cerium (see below) but nevertheless show a notably smaller lattice constant than that observed, we also examined the effect of oxygen vacancies by removing one O atom from each of the Ce19O32 and Ce44O80 models (Figure 1). We studied two clusters Ce19O31X, with an O vacancy either inside of the cluster (Xin) or in the outer shell in a {111} facet (Xout), and the cluster Ce44O79Xout, with a vacancy in the {111} facet. One O vacancy causes only a slight increase of the average Ce-Ce distance by 1-2 pm (Table 1). However, the immediate tetrahedral environment of the vacancy expands notably more, by ∼20 (Xin) and 30 pm (Xout), making these Ce-Ce distances even longer than those in the bulk. Removing a surface O causes stronger cluster deformation than removing an inner O because the surface Ce atoms may relax more freely. We emphasize that the overall relaxation is substantially larger for the nanoparticles than that for extended surfaces, for example, (111) surface relaxations upon vacancy formation are reported to be quite small.35 Thus, O vacancies appear to be a prerequisite for the lattice expansion of ceria particles beyond the bulk value. In other words, the observed lattice anomaly in (CeO2-x)n nanoparticles clearly provides evidence of their highly defective character. Nonstoichiometric ceria nanoparticles without any vacancies possess intrinsically Ce3+ cations, but this alone does not suffice to rationalize the observed expansion of the clusters. Moreover, a broad range of interatomic distances within nanoparticles with vacancies is expected, leaving the feature of one single lattice constant questionable. The inset of Figure 2 displays the binding energy Eb per Ce atom as a function of particle size, represented by the average coordination number N () of Ce atoms. Both the LDA+U and GGA+U values Eb show a nearly perfect linear correlation with the parameter and smoothly converge to the corresponding bulk values. These data allow predictions to be made for larger experimentally prepared particles, which are still beyond the feasibility of an ab initio treatment.

Figure 3. Electron localization function (ELF) plots in the (111) plane of bulk CeO2 (a) and the equivalent plane of bulk Ce2O3 (b) and of the Ce19O32 particle (c).

The spatial distribution of reduced/oxidized Ce cations is crucial for the reactivity of ceria materials. Magnetic moments on Ce cations µ(Ce) and core level Ce 3d energies from representative lowest energy LDA+U calculations36 are shown in Table 2. These µ(Ce) values clearly indicate that the spin density tends to be located on Ce centers that occupy more exposed (lower coordinated) edge and corner sites of the nanoparticles, whereas better coordinated Ce atoms are in the inner part of the clusters and on the facet positions remote from the edges. Thus, partially reduced Ce3+ cations preferably occupy low-coordinated positions on ceria nanoparticles. Since these species are mainly located on the surface, they directly affect the nanoparticle reactivity. The calculated energies of the core orbitals Ce 3d also allow for a clear distinction between Ce3+ and Ce4+ states and fully support the trend arising from the magnetic moments; Ce centers where f electrons are localized possess a notable upshift of the energies of 3d orbitals, as expected from the reduced charge in the ion. Nevertheless, because of the approximations involved, a more quantitative comparison with experimental binding energies is not possible. To substantiate the finding above, we compare the electron localization function (ELF)37 of the Ce19O32 particle with those of the bulk CeO2 and Ce2O3 references in Figure 3 (results for larger particles are very similar; also, there is hardly any difference between LDA+U and GGA+U profiles). A rather low ELF value between the Ce and O atoms is indicative of mainly polar ionic bonding in bulk CeO2 or Ce2O3. The ELF features of the nanoparticle are similar to those of the bulk references. Using the known ELF contours of the references, Ce3+ and Ce4+ cations may be distinguished; nearly spherical Ce4+ are located inside of the cluster, whereas the reduced Ce3+ ones reside in open positions outside. In summary, we have demonstrated that DFT+U calculations practicable for ceria nanoparticles approaching the size of experimentally treated species enable detailed insight into their structure and properties. In particular, the binding energy per Ce atom is shown to correlate linearly with the average coordination number of Ce, allowing predictions for particle

Letters sizes beyond the capabilities of current ab initio methods. The expansion of ceria nanoparticles with decreasing size is explicitly assigned to the presence of oxygen vacancies. For nonstoichiometric ceria particles without O vacancies, we also examined the spatial distribution of Ce3+/Ce4+ cations. Whereas the Ce4+ atoms prefer to reside at highly coordinated positions, the reduced cations tend to occupy corner and edge sites and thus are more likely to affect the reactivity of the nanoparticles. Thus, we have not only explored the electronic, energetic, and structural details of ceria nanocluster models of practical relevance, but we have also provided a foundation for emerging large-scale ab initio simulations of materials based on ceria nanocrystallites and similar nanostructures as well as chemical interactions with them. Acknowledgment. C.L. is grateful to the Alexander von Humboldt Foundation for a postdoctoral fellowship. Financial support has been provided by the Spanish Ministry of Education and Science (Projects CTQ2005-08459-CO2-01, UNBA05-33001), the Ramon y Cajal program (S.T.B.), and by Generalitat de Catalunya (Projects 2005SGR-00697, 2005 PEIR 0051/69, and Distincio´ GenCat granted to F.I.). A significant part of computer time was provided by the Barcelona Supercomputing Center. References and Notes (1) Fu, Q.; Saltsburg, H.; Flytzani-Stephanopoulos, M. Science 2003, 301, 935-938. (2) Trovarelli, A. Catal. ReV.sSci. Eng. 1996, 38, 439-520. (3) Carrettin, S.; Concepcio´n, P.; Corma, A.; Lo´pez Nieto, J. M.; Puntes, V. F. Angew. Chem. Int. Ed. 2004, 43, 2538-2540. (4) Sayle, T. X. T.; Parker, S. C.; Catlow, C. R. A. Surf. Sci. 1994, 316, 329-336. (5) Cordatos, H.; Ford, D.; Gorte, R. J. J. Phys. Chem. 1996, 100, 18128-18132. (6) Feng, X.; Sayle, D. C.; Wang, Z. L.; Paras, M. S.; Santora, B.; Sutorik, A. C.; Sayle, T. X. T.; Yang, Y.; Ding, Y.; Wang, X.; Her, Y.-S. Science 2006, 312, 1504-1508. (7) Martin, P.; Parker, S. C.; Sayle, D. C.; Watson, G. W. Nano Lett. 2007, 7, 543-546. (8) Anisimov, V. I.; Aryasetiawan, F.; Lichtenstein, A. I. J. Phys.: Condens. Matter 1997, 9, 767-808. (9) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Phys. ReV. B 1998, 57, 1505-1509. (10) Loschen, C.; Carrasco, J.; Neyman, K. M.; Illas, F. Phys. ReV. B 2007, 75, 035115/1-035115/8.

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